441 research outputs found
Quantization of (2+1)-spinning particles and bifermionic constraint problem
This work is a natural continuation of our recent study in quantizing
relativistic particles. There it was demonstrated that, by applying a
consistent quantization scheme to a classical model of a spinless relativistic
particle as well as to the Berezin-Marinov model of 3+1 Dirac particle, it is
possible to obtain a consistent relativistic quantum mechanics of such
particles. In the present article we apply a similar approach to the problem of
quantizing the massive 2+1 Dirac particle. However, we stress that such a
problem differs in a nontrivial way from the one in 3+1 dimensions. The point
is that in 2+1 dimensions each spin polarization describes different fermion
species. Technically this fact manifests itself through the presence of a
bifermionic constant and of a bifermionic first-class constraint. In
particular, this constraint does not admit a conjugate gauge condition at the
classical level. The quantization problem in 2+1 dimensions is also interesting
from the physical viewpoint (e.g. anyons). In order to quantize the model, we
first derive a classical formulation in an effective phase space, restricted by
constraints and gauges. Then the condition of preservation of the classical
symmetries allows us to realize the operator algebra in an unambiguous way and
construct an appropriate Hilbert space. The physical sector of the constructed
quantum mechanics contains spin-1/2 particles and antiparticles without an
infinite number of negative-energy levels, and exactly reproduces the
one-particle sector of the 2+1 quantum theory of a spinor field.Comment: LaTex, 24 pages, no figure
Path integral and pseudoclassical action for spinning particle in external electromagnetic and torsion fields
Starting from the Dirac equation in external electromagnetic and torsion
fields we derive a path integral representation for the corresponding
propagator. An effective action, which appears in the representation, is
interpreted as a pseudoclassical action for a spinning particle. It is just a
generalization of Berezin-Marinov action to the background under consideration.
Pseudoclassical equations of motion in the nonrelativistic limit reproduce
exactly the classical limit of the Pauli quantum mechanics in the same case.
Quantization of the action appears to be nontrivial due to an ordering problem,
which needs to be solved to construct operators of first-class constraints, and
to select the physical sector. Finally the quantization reproduces the Dirac
equation in the given background and, thus, justifies the interpretation of the
action.Comment: 18 pages, LaTeX. Small modifications, some references added. To be
published in International Journal of Modern Physics
Comments on spin operators and spin-polarization states of 2+1 fermions
In this brief article we discuss spin polarization operators and spin
polarization states of 2+1 massive Dirac fermions and find a convenient
representation by the help of 4-spinors for their description. We stress that
in particular the use of such a representation allows us to introduce the
conserved covariant spin operator in the 2+1 field theory. Another advantage of
this representation is related to the pseudoclassical limit of the theory.
Indeed, quantization of the pseudoclassical model of a spinning particle in 2+1
dimensions leads to the 4-spinor representation as the adequate realization of
the operator algebra, where the corresponding operator of a first-class
constraint, which cannot be gauged out by imposing the gauge condition, is just
the covariant operator previously introduced in the quantum theory.Comment: 6 page
Canonical and D-transformations in Theories with Constraints
A class class of transformations in a super phase space (we call them
D-transformations) is described, which play in theories with second-class
constraints the role of ordinary canonical transformations in theories without
constraints.Comment: 16 pages, LaTe
Two-dimensional metric and tetrad gravities as constrained second order systems
Using the Gitman-Lyakhovich-Tyutin generalization of the Ostrogradsky method
for analyzing singular systems, we consider the Hamiltonian formulation of
metric and tetrad gravities in two-dimensional Riemannian spacetime treating
them as constrained higher-derivative theories. The algebraic structure of the
Poisson brackets of the constraints and the corresponding gauge transformations
are investigated in both cases.Comment: replaced with revised version published in
Mod.Phys.Lett.A22:17-28,200
Canonical form of Euler-Lagrange equations and gauge symmetries
The structure of the Euler-Lagrange equations for a general Lagrangian theory
is studied. For these equations we present a reduction procedure to the
so-called canonical form. In the canonical form the equations are solved with
respect to highest-order derivatives of nongauge coordinates, whereas gauge
coordinates and their derivatives enter in the right hand sides of the
equations as arbitrary functions of time. The reduction procedure reveals
constraints in the Lagrangian formulation of singular systems and, in that
respect, is similar to the Dirac procedure in the Hamiltonian formulation.
Moreover, the reduction procedure allows one to reveal the gauge identities
between the Euler-Lagrange equations. Thus, a constructive way of finding all
the gauge generators within the Lagrangian formulation is presented. At the
same time, it is proven that for local theories all the gauge generators are
local in time operators.Comment: 27 pages, LaTex fil
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